Parallel Axis Theorem and Perpendicular Axis Theorem
The difference between parallel axis theorem and perpendicular axis theorem from the table given below:
Aspect | Parallel Axis Theorem | Perpendicular Axis Theorem |
|---|---|---|
Definition | Relates the moment of inertia about a parallel axis to the moment of inertia about the centroidal axis and the distance between them. | Relates the moment of inertia about an axis perpendicular to the plane of a two-dimensional object to the sum of its moments of inertia about two perpendicular axes lying in the plane. |
Applicability | Applicable to calculating the moment of inertia of a rigid body about any parallel axis, given the moment of inertia about its centroidal axis. | Applicable to calculating the moment of inertia of a two-dimensional object about an axis perpendicular to its plane, given its moments of inertia about two perpendicular axes lying in the plane. |
Formula | Iparallel = Icentroidal + md2 | Iz = Ix + Iy |
Example | Calculating the moment of inertia of a thin rod about an axis parallel to one end, given its moment of inertia about the centroidal axis. | Calculating the moment of inertia of a flat plate about an axis perpendicular to its plane, given its moments of inertia about two perpendicular axes lying in the plane. |
Dimensionality | Applicable to three-dimensional rigid bodies. | Applicable to two-dimensional objects. |
Ease of Application | Requires knowledge of the centroidal moment of inertia and the distance between the centroidal and parallel axes. | Requires knowledge of the moments of inertia about two perpendicular axes lying in the plane of the object. |
Widely Used in | Widely used in engineering and physics for analyzing the rotational motion of rigid bodies. | Less commonly used but still important for calculating moments of inertia in two-dimensional systems. |
Parallel Axis Theorem
Parallel axis theorem states that the moment of inertia of a rigid body about any axis parallel to its centroidal axis is equal to the sum of the body’s moment of inertia about its centroidal axis and the product of its mass and the square of the distance between the two axes.
In this article, we will understand the meaning of the parallel axis theorem, its history, proof, limitations and applications of parallel axis theorem.
Table of Content
- What is the Parallel Axis Theorem?
- What is the Formula of the Theorem of Parallel Axis?
- Parallel Axis Theorem Proof
- Limitations of Parallel Axis Theorem
- Application of Parallel Axis Theorem